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Sergeeva-Olga [200]
3 years ago
10

Write down in terms of n, an expression for the nth term

Mathematics
2 answers:
Hatshy [7]3 years ago
8 0

Answer:

The nth term will be:

a_n=-5n+30

Step-by-step explanation:

Given the sequence

25, 20, 15, 10, 5​

An Arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

Computing the common difference of all the adjacent terms

25,\:20,\:15,\:10,\:5

20-25=-5,\:\quad \:15-20=-5,\:\quad \:10-15=-5,\:\quad \:5-10=-5

As the difference between all the adjacent terms is the same and equal to

d=-5

Also, the first term is:

a_1=25

Hence, the nth term will be:

a_n=a_1+\left(n-1\right)d

a_n=-5\left(n-1\right)+25        ∵ a_1=25, d=-5

a_n=-5n+30

Therefore, the nth term will be:

a_n=-5n+30

pshichka [43]3 years ago
5 0

Answer:

Solution,

First term (a) = 25

Common difference (d) = Second term - first term = 20 - 25 = -5

Now,

nth term = a + (n - 1)d = 25 + (n - 1) (-5) = 25 - 5n +5 = 30 - 5n

The nth term of the series is 30 - 5n

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